Finite Group Databasebeta

← Group #10693480

Character table — Group #10693480

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111111111111122222222222222222222222244444444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order122222224444444434444444466666661212121212121212888888881212121212121212242424242424242424242424242424244444888812121212121212122424242424242424888888888888888822448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ911111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−iii−i−iii−i−i1111-1-1-1-111-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i−i−iii−i−iii-1-1-1-11111-1-111−i−iii
χ1111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiiiii−i−iii−i−i1111-1-1-1-1-1-111−i−iii
χ1211111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii−i−iii−i−iii-1-1-1-1111111-1-1ii−i−i
χ1311111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiiiii−i−iii−i−i-1-1-1-11111-1-111ii−i−i
χ1411111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii−i−iii−i−iii1111-1-1-1-111-1-1−i−iii
χ1511111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−iii−i−iii−i−i-1-1-1-1111111-1-1−i−iii
χ1611111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i−i−iii−i−iii1111-1-1-1-1-1-111ii−i−i
χ1722222222222222222-2-2-2-2-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000002222-2-2-2-20000000000000000
χ1822222222222222222-2-2-2-2-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-2-2-222220000000000000000
χ192222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ202222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ212222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ222222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ2322222222-2-2-2-2-2-2-2-22-2-22222-2-22222222-2-2-2-2-2-2-2-200000000-2-2-2-2222200000000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2422222222-2-2-2-2-2-2-2-22-2-22222-2-22222222-2-2-2-2-2-2-2-200000000-2-2-2-222220000000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2522222222-2-2-2-2-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-1111111112i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii22-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-1111111112i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-2-222−2i−2i2i2i1111-1-1-1-1iiii−i−i−i−i000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-111111111−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i22-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-111111111−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-2-2222i2i−2i−2i1111-1-1-1-1−i−i−i−iiiii000000000000000000000000
χ29222-2-2-2-2222-2-2-2-222200000000222-2-2-2-22222-2-2-2-222−2−222−2−2000000002222−2−2−2−22222−2−2−2−20000000000000000000000002i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i200000000
χ30222-2-2-2-2222-2-2-2-222200000000222-2-2-2-22222-2-2-2-222−2−222−2−2000000002222−2−2−2−22222−2−2−2−2000000000000000000000000−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i200000000
χ31222-2-2-2-2222-2-2-2-222200000000222-2-2-2-22222-2-2-2-2−2−222−2−22200000000−2−2−2−22222−2−2−2−222220000000000000000000000002i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i200000000
χ32222-2-2-2-2222-2-2-2-222200000000222-2-2-2-22222-2-2-2-2−2−222−2−22200000000−2−2−2−22222−2−2−2−22222000000000000000000000000−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i200000000
χ33222-2-2-2-22-2-22222-2-2200000000222-2-2-2-2-2-2-2-22222−i2−i2i2i2i2i2−i2−i200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i20000000000000000000000002-2-220000−i2−i2i2i2i2i2−i2−i200000000
χ34222-2-2-2-22-2-22222-2-2200000000222-2-2-2-2-2-2-2-22222−i2−i2i2i2i2i2−i2−i200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2000000000000000000000000-222-20000i2i2−i2−i2−i2−i2i2i200000000
χ35222-2-2-2-22-2-22222-2-2200000000222-2-2-2-2-2-2-2-22222i2i2−i2−i2−i2−i2i2i200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i20000000000000000000000002-2-220000i2i2−i2−i2−i2−i2i2i200000000
χ36222-2-2-2-22-2-22222-2-2200000000222-2-2-2-2-2-2-2-22222i2i2−i2−i2−i2−i2i2i200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2000000000000000000000000-222-20000−i2−i2i2i2i2i2−i2−i200000000
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χ3822-22-22-2-22i−2i2i−2i2i−2i2i−2i22-22i−2i2i−2i2-22-2-22-22-22i2i−2i−2i2i−2i2i−2i0000000022-2-22i−2i2i−2i000000000000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13
χ3922-22-22-2-22i−2i2i−2i2i−2i2i−2i2-22−2i2i−2i2i-222-2-22-22-22i2i−2i−2i2i−2i2i−2i00000000-2-222−2i2i−2i2i00000000000000002-22i−2i000022-2-22i2i−2i−2i00000000000000000000000000000000
χ4022-22-22-2-22i−2i2i−2i2i−2i2i−2i2-22−2i2i−2i2i-222-2-22-22-22i2i−2i−2i2i−2i2i−2i00000000-2-222−2i2i−2i2i0000000000000000-22−2i2i0000-2-222−2i−2i2i2i00000000000000000000000000000000
χ4122-22-22-2-22i−2i2i−2i2i−2i2i−2i-1-22−2i2i−2i2i-22-111-11-11−i−iii−ii−ii0000000011-1-1i−ii−iζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ232-22i−2i0000-1-111−i−iiiζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23000000000000000000000000
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χ4322-22-22-2-22i−2i2i−2i2i−2i2i−2i-1-22−2i2i−2i2i-22-111-11-11−i−iii−ii−ii0000000011-1-1i−ii−i−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ232-22i−2i0000-1-111−i−iii−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23000000000000000000000000
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χ4522-22-22-2-2−2i2i−2i2i−2i2i−2i2i22-2−2i2i−2i2i2-22-2-22-22-2−2i−2i2i2i−2i2i−2i2i0000000022-2-2−2i2i−2i2i000000000000000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23
χ4622-22-22-2-2−2i2i−2i2i−2i2i−2i2i22-2−2i2i−2i2i2-22-2-22-22-2−2i−2i2i2i−2i2i−2i2i0000000022-2-2−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23
χ4722-22-22-2-2−2i2i−2i2i−2i2i−2i2i2-222i−2i2i−2i-222-2-22-22-2−2i−2i2i2i−2i2i−2i2i00000000-2-2222i−2i2i−2i00000000000000002-2−2i2i000022-2-2−2i−2i2i2i00000000000000000000000000000000
χ4822-22-22-2-2−2i2i−2i2i−2i2i−2i2i2-222i−2i2i−2i-222-2-22-22-2−2i−2i2i2i−2i2i−2i2i00000000-2-2222i−2i2i−2i0000000000000000-222i−2i0000-2-2222i2i−2i−2i00000000000000000000000000000000
χ4922-22-22-2-2−2i2i−2i2i−2i2i−2i2i-1-222i−2i2i−2i-22-111-11-11ii−i−ii−ii−i0000000011-1-1−ii−ii−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ132-2−2i2i0000-1-111ii−i−i−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13000000000000000000000000
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χ5222-22-22-2-2−2i2i−2i2i−2i2i−2i2i-1-222i−2i2i−2i-22-111-11-11ii−i−ii−ii−i0000000011-1-1−ii−iiζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13-222i−2i000011-1-1−i−iii−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13000000000000000000000000
χ532-222-2-22-22i−2i2i−2i−2i2i−2i2i22-2−2i2i2i−2i-22-22-22-2-222i−2i2i−2i−2i2i2i−2i000000002-22-2−2i2i2i−2i00000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ542-222-2-22-22i−2i2i−2i−2i2i−2i2i22-2−2i2i2i−2i-22-22-22-2-222i−2i2i−2i−2i2i2i−2i000000002-22-2−2i2i2i−2i000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ552-222-2-22-22i−2i2i−2i−2i2i−2i2i2-222i−2i−2i2i2-2-22-22-2-222i−2i2i−2i−2i2i2i−2i00000000-22-222i−2i−2i2i000000000000000000000000000000000000000000000000000000002-22i−2i0000
χ562-222-2-22-22i−2i2i−2i−2i2i−2i2i2-222i−2i−2i2i2-2-22-22-2-222i−2i2i−2i−2i2i2i−2i00000000-22-222i−2i−2i2i00000000000000000000000000000000000000000000000000000000-22−2i2i0000
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χ1174-4-4-4-444444-4-444-4-4-20000000022-222-2-2-222-2-2-222−2i22i22i2−2i2−2i22i22i2−2i200000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000000000000000000000000000000000000000
χ1184-4-4-4-444444-4-444-4-4-20000000022-222-2-2-222-2-2-2222i2−2i2−2i22i22i2−2i2−2i22i200000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000000000000000000000000000000000000000
χ1194-4-4-4-4444-4-444-4-444-20000000022-222-2-22-2-2222-2-222−22−2222−222222−2200000000−222−22−2−22−222−22−2−22000000000000000000000000000000000000000000000000
χ1204-4-4-4-4444-4-444-4-444-20000000022-222-2-22-2-2222-2-2−222222−2222−22−2222000000002−2−22−222−22−2−22−222−2000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.